Question

What is the equation of a line that contains (-2,5) and is perpendicular to y=(1/2)x + 6?

Answer 1

Answer: The equation ud y=-2x+1.

Step-by-step explanation: The perpendicular lines the gradient products of -1 which means when we multiply the gradient of line 1 with that of line 2 we must get -1. Here the gradient is 1/2 so the gradient of the other line is -2 and we are given the x and y we have to find c and write the equation. y=mx+c

5=-2(-2)+c

c=1

y=-2x+1

Answer 2

Answer:

y = - 2x + 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = $\frac{1}{2}$ x + 6 ← is in slope- intercept form

with slope m = $\frac{1}{2}$

Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{\frac{1}{2} }$ = - 2, thus

y = - 2x + c ← is the partial equation

To find c substitute (- 2, 5) into the partial equation

5 = 4 + c ⇒ c = 5 - 4 = 1

y = - 2x + 1 ← equation of line